Find minimum number of Substrings with unique characters

Given string ‘s’, the task is to divide a given string s into multiple substrings, with each substring containing only unique characters. This means that no character should be repeated within a single substring. The goal is to find the minimum number of such substrings required to satisfy this condition.

Examples:

Input: s = “abacaba”
Output: 4
Explanation: Two possible partitions are (“a”, “ba”, “cab”, “a”) and (“ab”, “a”, “ca”, “ba”). It can be shown that 4 is the minimum number of substrings needed.

Input: s = “ssssss”
Output: 6
Explanation: The only valid partition is (“s”, “s”, “s”, “s”, “s”, “s”).

Naive Approach: The basic way to solve the problem follows the below idea:

• We initialize an empty set and iterate through the given string. For each character encountered, we check if it is already present in the set. 
• If it is, this means that we need to start a new substring since the current substring has a repeated character. We increase our answer variable and clear the set to start a new substring. We then add the current character to the set.
• After iterating through the entire string, the value of the answer variable gives us the minimum number of substrings required to partition the given string such that each substring has unique characters.

Below is the implementation for the above approach:

C++

// C++ program to Finding minimum number
// of Substrings with unique Characters
#include <bits/stdc++.h>
using namespace std;

// Function to Find Minimum Number of
// Substrings with Unique Characters
int partitionString(string s)
{

    // Create an unordered set to
    // store unique characters
    unordered_set<char> st;

    // Initialize the answer
    // variable to 1
    int ans = 1;

    // Iterate through the given string
    for (int i = 0; i < s.size(); i++) {

        // Check if the current character
        // is already present in the set
        if (st.find(s[i]) != st.end()) {

            // If it is, increment the
            // answer variable and clear
            // the set to start a
            // new substring
            ans++;
            st.clear();
        }

        // Add the current character
        // to the set
        st.insert(s[i]);
    }

    // Return the answer variable, which
    // gives the minimum number
    // of substrings required
    return ans;
}

// Drivers code
int main()
{
    string S = "abacaba";

    // Function Call
    cout << "Minimum Number of Substrings with Unique "
            "Characters: "
         << partitionString(S);

    return 0;
}

Java

// Java program to Finding Minimum Number of Substrings with
// Unique Characters
import java.util.*;

// Function to Find Minimum Number of Substrings with Unique
// Characters
class GFG {
    static int partitionString(String s)
    {
        // Create a HashSet to store unique characters
        Set<Character> set = new HashSet<>();
        // Initialize the answer variable to 1
        int ans = 1;
        // Iterate through the given string
        for (int i = 0; i < s.length(); i++) {
            // Check if the current character is already
            // present in the set
            if (set.contains(s.charAt(i))) {
                // If it is, increment the answer variable
                // and clear the set to start a new
                // substring
                ans++;
                set.clear();
            }
            // Add the current character to the set
            set.add(s.charAt(i));
        }
        // Return the answer variable, which gives the
        // minimum number of substrings required
        return ans;
    }

    public static void main(String[] args)
    {
        String S = "abacaba";

        System.out.print(partitionString(S));
    }
}
// This code is contributed by Ravi Singh

Python3

# Function to Find Minimum Number of
# Substrings with Unique Characters
def partitionString(s):
    # Create an unordered set to
    # store unique characters
    st = set()

    # Initialize the answer
    # variable to 1
    ans = 1

    # Iterate through the given string
    for i in range(len(s)):
        # Check if the current character
        # is already present in the set
        if s[i] in st:
            # If it is, increment the
            # answer variable and clear
            # the set to start a
            # new substring
            ans += 1
            st.clear()

        # Add the current character
        # to the set
        st.add(s[i])

    # Return the answer variable, which
    # gives the minimum number
    # of substrings required
    return ans


# Drivers code
S = "abacaba"

# Function Call
print("Minimum Number of Substrings with Unique Characters:", partitionString(S))

C#

// C# program to Finding Minimum Number of Substrings with
// Unique Characters

using System;
using System.Collections.Generic;

public class GFG {

    static int partitionString(string s)
    {
        // Create a HashSet to store unique characters
        HashSet<char> set = new HashSet<char>();
        // Initialize the answer variable to 1
        int ans = 1;
        // Iterate through the given string
        for (int i = 0; i < s.Length; i++) {
            // Check if the current character is already
            // present in the set
            if (set.Contains(s[i])) {
                // If it is, increment the answer variable
                // and clear the set to start a new
                // substring
                ans++;
                set.Clear();
            }
            // Add the current character to the set
            set.Add(s[i]);
        }
        // Return the answer variable, which gives the
        // minimum number of substrings required
        return ans;
    }

    static public void Main()
    {

        // Code
        String S = "abacaba";

        Console.Write("Minimum Number of Substrings with Unique Characters: " + partitionString(S));
    }
}

// THis code is contributed by karthik

Javascript

// JavaScript program to Finding minimum number
// of Substrings with unique Characters

// Function to Find Minimum Number of Substrings with Unique
// Characters
function partitionString(s) {
    // Create a set to store unique characters
    let st = new Set();

    // Initialize the answer
    // variable to 1
    let ans = 1;

    // Iterate through the given string
    for (let i = 0; i < s.length; i++) {

        // Check if the current character
        // is already present in the set
        if (st.has(s[i])) {

            // If it is, increment the
            // answer variable and clear
            // the set to start a
            // new substring
            ans++;
            st.clear();
        }

        // Add the current character
        // to the set
        st.add(s[i]);
    }

    // Return the answer variable, which
    // gives the minimum number
    // of substrings required
    return ans;
}

// Driver code
let S = "abacaba";

// Function Call
console.log(
    "Minimum Number of Substrings with Unique Characters: "
    + partitionString(S));

Output

Minimum Number of Substrings with Unique Characters: 4

Time Complexity: O(n) where n is the length of the input string.
Auxiliary Space: O(n) in the worst case This is because we store each character of the input string in the hash set, and in the worst case, all characters of the string are unique. 

Efficient Approach: To solve the problem using a Greedy approach follow the below idea:

To solve this problem, we need to keep track of the last occurrence of each character in the string s. Whenever we encounter a repeated character, we know that the current substring contains a character that is repeated, so we need to start a new substring. We can determine the start of the new substring by setting the value of start to the index of the repeated character. We also increased the value of ans to indicate that we have started a new substring.

Below are the steps for the above approach:

• Create an array list of size 26 to store the last index of each character (initially set to -1).
  Initialize the starting index of the current substring to 0.
• Initialize the answer variable ans to 1.
• Iterate through the given string s:
  • Get the index of the current character in the array by subtracting ‘a’ from it.
  • Check if the current character is already present in the current substring by comparing its last index with the starting index of the current substring.
  • If it is, increment the answer variable ans and update the starting index of the new substring to the current index.
• Update the last index of the current character in the array with the current index.
• Return the answer variable ans, which gives the minimum number of substrings required.

Below is the implementation for the above approach:

C++

// C++ program to Finding Minimum
// Number of Substrings with
// Unique Characters

#include <bits/stdc++.h>
using namespace std;

// Function to Find Minimum Number of
// Substrings with Unique characters
int partitionString(string s)
{

    // Create an array to store the
    // last index of each character
    vector<int> last(26, -1);

    // Initialize the starting index
    // of the current substring to 0
    int start = 0;

    // Initialize the answer variable to 1
    int ans = 1;

    // Iterate through the given string
    for (int i = 0; i < s.length(); i++) {

        // Get the index of the current
        // character in the array
        int index = s[i] - 'a';

        // Check if the current character
        // is already present in the
        // current substring
        if (last[index] >= start) {

            // If it is, increment the answer
            // variable and update the
            // starting index of the
            // new substring
            ans++;
            start = i;
        }

        // Update the last index
        // of the current character
        last[index] = i;
    }

    // Return the answer variable, which
    // gives the minimum number of
    // substrings required
    return ans;
}

// Drivers code
int main()
{

    string S = "abacaba";

    // Function Call
    cout << "Minimum Number of Substrings with Unique "
            "Characters: "
         << partitionString(S);

    return 0;
}

Java

// Java program to Finding Minimum Number of Substrings with
// Unique Characters
import java.util.*;

// Function to Find Minimum Number of Substrings with Unique
// Characters

class GFG {
    static int partitionString(String s)
    {
        // Create an array to store the last index of each
        // character
        int[] last = new int[26];
        Arrays.fill(last, -1);

        // Initialize the starting index of the current
        // substring to 0
        int start = 0;

        // Initialize the answer variable to 1
        int ans = 1;

        // Iterate through the given string
        for (int i = 0; i < s.length(); i++) {
            // Get the index of the current character in the
            // array
            int index = s.charAt(i) - 'a';

            // Check if the current character is already
            // present in the current substring
            if (last[index] >= start) {
                // If it is, increment the answer variable
                // and update the starting index of the new
                // substring
                ans++;
                start = i;
            }

            // Update the last index of the current
            // character
            last[index] = i;
        }

        // Return the answer variable, which gives the
        // minimum number of substrings required
        return ans;
    }

    public static void main(String[] args)
    {

        String S = "ssssss";

        System.out.print(partitionString(S));
    }
}
// This code is contributed by Ravi Singh

Python3

# Function to Find Minimum Number of
# Substrings with Unique characters
def partitionString(s):
    # Create an array to store the
    # last index of each character
    last = [-1] * 26

    # Initialize the starting index
    # of the current substring to 0
    start = 0

    # Initialize the answer variable to 1
    ans = 1

    # Iterate through the given string
    for i in range(len(s)):
        # Get the index of the current
        # character in the array
        index = ord(s[i]) - ord('a')

        # Check if the current character
        # is already present in the
        # current substring
        if last[index] >= start:
            # If it is, increment the answer
            # variable and update the
            # starting index of the
            # new substring
            ans += 1
            start = i

        # Update the last index
        # of the current character
        last[index] = i

    # Return the answer variable, which
    # gives the minimum number of
    # substrings required
    return ans


# Drivers code
if __name__ == '__main__':
    S = "abacaba"

    # Function Call
    print("Minimum Number of Substrings with Unique Characters: ", partitionString(S))

C#

using System;
using System.Collections.Generic;

public class Program
{
  // Function to find minimum number of substrings with unique characters
  public static int PartitionString(string s)
  {
    // Create a dictionary to store the last index of each character
    Dictionary<char, int> last = new Dictionary<char, int>();

    // Initialize the starting index of the current substring to 0
    int start = 0;

    // Initialize the answer variable to 1
    int ans = 1;

    // Iterate through the given string
    for (int i = 0; i < s.Length; i++)
    {
      char c = s[i];

      // Check if the current character is
      // already present in the current substring
      if (last.ContainsKey(c) && last >= start)
      {
        // If it is, increment the answer variable and
        // update the starting index of the new substring
        ans++;
        start = i;
      }

      // Update the last index of the current character
      last = i;
    }

    // Return the answer variable, which gives
    // the minimum number of substrings required
    return ans;
  }

  // Driver's code
  public static void Main()
  {
    string S = "abacaba";

    // Function call
    Console.WriteLine("Minimum Number of Substrings with Unique Characters: " + PartitionString(S));
  }
}
// This code is contributed by Prajwal Kandekar

Javascript

// JavaScript program to Finding Minimum
// Number of Substrings with
// Unique Characters

function partitionString(s) {

  // Create an array to store the
  // last index of each character
  const last = new Array(26).fill(-1);

  // Initialize the starting index
  // of the current substring to 0
  let start = 0;

  // Initialize the answer variable to 1
  let ans = 1;

  // Iterate through the given string
  for (let i = 0; i < s.length; i++) {

    // Get the index of the current
    // character in the array
    const index = s.charCodeAt(i) - 97;

    // Check if the current character
    // is already present in the
    // current substring
    if (last[index] >= start) {

      // If it is, increment the answer
      // variable and update the
      // starting index of the
      // new substring
      ans++;
      start = i;
    }

    // Update the last index
    // of the current character
    last[index] = i;
  }

  // Return the answer variable, which
  // gives the minimum number of
  // substrings required
  return ans;
}

// Example usage
const S = "abacaba";
console.log(`Minimum Number of Substrings with Unique Characters: ${partitionString(S)}`);

Output

Minimum Number of Substrings with Unique Characters: 4

Time Complexity: O(n) where n is the length of the input string.
Auxiliary Space: O(1)